The Hertz paper

Author: ulfarsson

_papers/2023-04-06-foata.md

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+---
+title: 'Turning cycle restrictions into mesh patterns via Foata's fundamental transformation'
+
+journal: Submitted
+
+authors:
+- claesson
+- ulfarsson
+
+projects:
+
+---
+![A tree]({{site.baseurl}}/assets/img/hertz.png){:align="right" height="200px"}
+    An adjacent q-cycle is a natural generalization of an adjacent
+    transposition. We show that the number of adjacent q-cycles in a
+    permutation maps to the sum of occurrences of two mesh patterns under
+    Foata's fundamental transformation. As a corollary we resolve
+    Conjecture 3.14 in the paper ''From Hertzprung's problem to
+    pattern-rewriting systems'' by the first author.
+
+    This work was started at Schloss Dagstuhl (Leibniz-Zentrum fur Informatik), seminar 23121, and we thank the institute and the organizers for giving us the opportunity to participate.
+<!-- The paragraph above is an adaptation of the abstract. 2023-04-06 -->
+
+## Download the paper
+<!-- - [{{ page.journal }}](https://cs.uwaterloo.ca/journals/JIS/VOL20/Bean/bean2.html) -->
+- [arXiv](https://arxiv.org/abs/2303.17931)
+
+## Presentations